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Theorem sum-subarray

m0 + m1 ≤ n, n ≤ # ar ⊦ sum(subarray(ar, 0, n), m0, m1) = sum(ar, m0, m1)

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by: max-sum-keep-current-max, max-sum-new-current-max, max-sum-next-less-zero, suffix-max-sum-reset, suffix-max-sum-step,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 4
Used lemmas: sum-succ, sum-zero,
Used spec theorems:
- Used simplifier rules:
  - int-basic2/add-c
  - int-basic2/add-a
  - int-basic2/add-in
  - nat-basic/add-base
  - array-copy/int-array/subarray-at
  - nat/fle-01
  - nat/let
  - nat/fle
  - nat-basic/f
  - nat-basic/c
  - nat/le-ls-simp
  - nat/succ-01
  - nat-basic/a
  - nat/lels
  - array-copy/int-array/size-subarray
  - nat-basic/succ
  - nat/lels-03